Due to their prevalent mechanical, electrical, and chemical properties, to name a few, triply periodic minimal surfaces (TPMS), a class of architected cellular materials, have attracted significant attention recently, where one of the major applications of these materials is biomimetic scaffold design, specifically in fabrication of biomimetic porous scaffolds [1]. However, TPMS lattices are computationally expensive to model explicitly when used in latticing various structures for enhanced multifunctionality, and hence the need to develop accurate yield surfaces in order to capture their plastic behavior in a homogenized approach. This study numerically investigates five different sheet-based TPMS lattices, which are Schoen’s I-WP, Gyroid, Diamond, F-RD and Primitive. The simulations are based on a single unit cell of each lattice under periodic boundary conditions, assuming an elastic-perfectly plastic behavior of the base material, at a relative density of 13%. To account for the different loading conditions, the Lode parameter (L) is used [2]. The effect of L is studied over a range of mean stress values where the results show that the effect of L on the effective yield surface of each lattice varies greatly (from significant to insignificant effect of L). Based on these findings, a generalized initial yield criterion that incorporates L is proposed in this work, where the criterion is validated against numerical results in five different loading conditions (axisymmetric, biaxial, uniaxial + shear, hydrostatic + shear and double shear) for each lattice. The proposed yield criterion accurately predicts the initial yielding of all these lattices in all the loading conditions considered, outperforming other well-established yield criteria currently proposed in literature for cellular materials.